Can gluten sensitivity cause you to catch viruses, bacterial infections, etc. more easily?

It seems like I'm always coming down with a cold or swine flu or something. If it's out there, I will catch it. I'm trying to narrow down why this is. I'm always washing and Purelling my hands, staying away from sick people, etc. I had an autoimmune disorder when I was little, but I'm in remission. I know that my immune system just isn't as good as everybody else, but I don't think that accounts for how often I get sick. I also cannot change my diet or exercise without catching something. That's been another red flag for me. Could it be gluten sensitivity or something else? I have several GS symptoms already, but my doc ruled it out with a blood test that they are now finding are inaccurate. Any ideas?